Weakly prime ternary subsemimodules of ternary semimodules

In this paper we introduce the concept of weakly prime ternary subsemimodules of a ternary semimodule over a ternary semiring and obtain some characterizations of weakly prime ternary subsemimodules. We prove that if N is a weakly prime subtractive ternary subsemimodule of a ternary R-semimodule M, then either N is a prime ternary subsemimodule or (N:M)(N:M)N=0. If N is a Q-ternary subsemimodule of a ternary R-semimodule M, then a relation between weakly prime ternary subsemimodules of M containing N and weakly prime ternary subsemimodules of the quotient ternary R-semimodule M/N(Q) is obtained.